Types Of Embedded Options

Embedded options in a bond allow an issuer to (1) manage interest rate risk and/or (2) issue the bonds at an attractive coupon rate. The embedded options can be a simple call or put option, or more complex options such as provisions for a sinking fund or an estate put.

Simple Options

Callable bonds give the issuer the option to call back the bond; the investor is short the call option. Most callable bonds have a call protection period during which the bond cannot be called. The call option can be a European style option (whereby the option can only be exercised on a single day immediately after the protection period), an American style option (whereby the option can be exercised at any time after the protection period), or even a Bermudan style option (whereby the option can be exercised at fixed dates after the protection period).

Putable bonds allow the investor to put (sell) the bond back to the issuer prior to maturity. The investor is long the underlying put option. A related bond is an extendible bond, which allows the investor to extend the maturity of the bond.

An extendible bond can be evaluated as a putable bond with longer maturity (i.e., the maturity if the bond is extended). A two year, 3% bond extendible for an additional year at the same coupon rate would be valued the same as an otherwise identical three year putable (European style) bond with a protection period of two years.

Complex Options

More complex options include:

An estate put which includes a provision that allows the heirs of an investor to put the bond back to the issuer upon the death of the investor. The value of this contingent put option is inversely related to the investor’s life expectancy; the shorter the life expectancy, the higher the value. Sinking fund bonds (sinkers) which require the issuer to set aside funds periodically to retire the bond (a sinking fund).

This provision reduces the credit risk of the bond. Sinkers typically have several related issuer options (e.g., call provisions, acceleration provisions, and delivery options).

In essence, the holder of a callable bond owns an option free (straight) bond and is also short a call option written on the bond. The value of the embedded call option ($V_{call}$) is, therefore, simply the difference between the value of a straight ($V_{straight}$) bond and the value of the comparable callable bond ($V_{callable}$):

Conversely, investors are willing to pay a premium for a putable bond since its holder effectively owns an option free bond plus a put option. The value of a putable bond can be expressed as:

Rearranging, the value of the embedded put option can be stated as: